IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v110y1982i3p535-549.html
   My bibliography  Save this article

Random walk on a random walk

Author

Listed:
  • Kehr, K.W.
  • Kutner, R.

Abstract

The authors investigate the random walk of a particle on a one-dimensional chain which has been constructed by a random-walk procedure. Exact expressions are given for the mean-square displacement and the fourth moment after n steps. The probability density after n steps is derived in the saddle-point approximation, for large n. These quantities have also been studied by numerical simulation. The extension to continuous time has been made where the particle jumps according to a Poisson process. The exact solution for the self-correlation function has been obtained in the Fourier and Laplace domain. The resulting frequency-dependent diffusion coefficient and incoherent dynamical structure factor have been discussed. The model of random walk on a random walk is applied to self-diffusion in the concentrated one-dimensional lattice gas where the correct asymptotic behavior is found.

Suggested Citation

  • Kehr, K.W. & Kutner, R., 1982. "Random walk on a random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 110(3), pages 535-549.
  • Handle: RePEc:eee:phsmap:v:110:y:1982:i:3:p:535-549
    DOI: 10.1016/0378-4371(82)90067-X
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843718290067X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/0378-4371(82)90067-X?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kehr, K.W. & Haus, J.W., 1978. "On the equivalence between multistate-trapping and continuous-time random walk models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 93(3), pages 412-426.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kutner, Ryszard & Świtała, Filip, 2004. "Remarks on the possible universal mechanism of the non-linear long-term autocorrelations in financial time-series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 244-251.
    2. Balakrishnan, V. & Van den Broeck, C., 1995. "Transport properties on a random comb," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 217(1), pages 1-21.
    3. Spišák, Daniel, 1994. "Two-dimensional diffusion of particles with dipolar-like interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 209(1), pages 42-50.
    4. Muszkieta, Monika & Janczura, Joanna & Weron, Aleksander, 2021. "Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    5. Huckaby, Dale A. & Hubbard, Joseph B., 1983. "A random walk on a random channel with absorbing barriers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 122(3), pages 602-610.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vlad, Marcel Ovidiu, 1994. "Non-Markovian approach for anomalous diffusion with infinite memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(2), pages 167-176.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:110:y:1982:i:3:p:535-549. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.